The game proposed in Numberplay this week (a regular feature of the blog Wordplay) is about arranging 16 plates in a circle so that any two adjacent plates' numbers sum to a perfect square. While I find the puzzle fun to think about, the solution being located at the end of the post makes it a little too tantalizing to just scroll down. But to prevent you from accidentally doing so, there are some wonderful solutions to the last Numberplay, a classic puzzle about distributing a fixed amount of water evenly amongst three differently sized cups. The solutions featured are not just numerical, but also visual, and many of them come from readers. In addition, not just one visual solution is presented. Rather, Antonick puts forth a nice solution that involves linear programming in three dimensions. Although only about a dozen readers commented on this post, their comments are almost as interesting as the post itself. For those who wish to follow the comments on a regular basis, check out the Numberplay Comments Fix, a great little bookmark that alters the way the comments are viewed so that latex can be seen easily.

A video entitled Mystery Math Teacher 2000 created by two math professors from Grand Valley State University went viral this last month with over 30,000 views. The video critiqued a Khan Academy Lesson on negative numbers and has now spawned a competition called MTT2K (sponsored in part by another blogger Dan Meyer) whose winner will receive a US$750.00 prize. Whether Salman Khan was flattered and/or frustrated by this snarky commentary, he quickly replaced the lesson with an improved version. Dr. Talbert discusses the pros and cons of Khan's videos, saying that there is not anything wrong with having videos that feature procedural knowledge (as opposed to conceptual). But he adds "As Dave (one of the commentators on the video) has explained, the snarkiness of their video may not rub everyone the right way, but Khan Academy has an almost impenetrable veneer of rightness about it that only biting satire could cut through." Dr. Talbert makes the distinction between "learning about a topic" and "learning the topic", and opines that Khan Academy is best for the former. Talbert explains that he has used Khan's videos, but thinks they are not a replacement for the relationship between student and teacher. While the blogger asserts that he's "not a Khan Academy hater," he also isn't "an uncritical fan." Readers might also be interested in Sal Khan's response to some of the criticisms that were posted in the Washington Post's blog, Answer Sheet.

That's the question posed by Hacker, a retired political science professor, on the front page of the Times's opinion section. Hacker's answer? No! He writes that he once accepted the arguments for requiring algebra, "But the more I examine them, the clearer it seems that they are largely or wholly wrong--unsupported by research or evidence, or based on wishful logic." He does think that students need quantitative skills, but feels that algebra blocks the progress of many otherwise capable students, causing them to drop out of high school or college. Naturally this hurts them, but it also hurts society because of the lost talent. He admits that higher math is necessary to modern life and to science and technology majors, but not to most others (and adds the head-scratcher: "(How many college graduates remember what Fermat's dilemma was all about?).") He ends his opinion piece with: "Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer."

The provocative piece has also elicited many comments on The New York Times site, as well as articles and blogs on other sites, such as Huffington Post, Washington Post, CNN, and National Review. One response is from the 2012 AMS-AAAS Media Fellow, Evelyn Lamb, who is a recent PhD from Rice University and is spending her summer writing for Scientific American. Lamb rebuts many of Hacker's arguments about requiring algebra, and writes that the problem-solving ability acquired in math courses is useful. While she does agree that people may not need algebra to do their jobs, she points out that getting an education is more than just acquiring skills for a job or career. She concludes with: "Math education needs to improve, but if illiteracy were on the rise, I don't think we'd be talking about eliminating reading from the curriculum." Lamb was also interviewed on NPR's The Takeaway.

"What's most interesting about the 100-country International Mathematical Olympiad (IMO) that took place [4-16 July] in Mar del Plata, Argentina, was not that Asian students won the top prizes---they often do---but the fact that the event went virtually unnoticed in our part of the world," notes this journalist. "Our TV networks are already sending teams of reporters to cover javelin throws, archery and synchronized swimming competitions at the upcoming London Olympics, but few---if any---sent a correspondent to the Mar del Plata math tournament." The winning teams of the 53rd IMO were South Korea in First Place, followed by China, U.S., Russia, Canada, Thailand and Singapore. The top prize to an individual went to Lim Jeck, 17, of Singapore, "who won a gold medal with a perfect score and became an instant media star in his home country." In Oppenheimer's opinion, "In the growing East vs. West battle for the best academic standards, we in the media share a large of responsibility for not putting education at the top of the public agenda." Indeed, there was no major media attention given to the IMO in the U.S., and now, during the Summer Olympics in London, might be a good time to ponder the disparity between media coverage of sport and mathematics achievements.

"Labs at the University of Maryland, College Park (U.M.), the University of Illinois at Urbana–Champaign and the University of Texas–Pan American are employing a new educational model for math in which professors mentor postdocs and graduate students, who in turn mentor undergraduates, to create visualizations of geometric structures, facilitate undergraduate research and participate in community outreach." The programming of the software needed to create the visualizations helps improve researchers understand the concepts, and the images themselves help others to appreciate and better understand math as a science and art. the creators of these geometry labs are spreading awareness of the images to non-math majors, future math teachers,elementary school students. the article includes a slideshow and video. See the Experimental Geometry Lab (EGL) at University of Maryland, the Illinois Geometry Lab (IGL) at the University of Illinois Urbana-Champaign, and the Experimental Algebra and Geometry Lab (EAGL) at University of Texas–Pan-American.

(Image: "Loxodrome," by Paul Nylander. A loxodrome is a spiral that arises from following a particular direction from the north or south pole of a sphere, meeting every line of latitude in the same (non-right) angle. This is a stereographic projection of a loxodrome onto a plane. A stereographic projection takes a sphere onto a plane in a prescribed way. --- Paul Nylander (bugman123.com) / Experimenal Geometry Lab (EGL).

The fun-loving folks at Google program some surprises, called Easter eggs, for searchers of certain phrases. In this case, people who search on the phrase Conway's Game of Life get the results that one would expect, but also get a bonus: The cellular automata game---invented by mathematician John Conway and involving cells that can live, multiply, or die, depending on the status of neighboring cells---playing itself out on their screens.

Which mathematical equations did not make it into Ian Stewart's recent book, "17 Equations That changed the World"?Stewart notes google search algorithms and "better equations to describe the actual function of financial markets," but focuses on equations related to mathematical biology. Stewart says, "There are at least three areas ripe for an effective mathematical model: development (from egg to adult), ecosystems, and evolution. I think we will need a new concept of 'equation', though---one that incorporates all of the genetic information in DNA, and other biochemical systems, and combines that with many other influences from the outside world."

Today's manufacturing work requires strong math skills, and employers can't find good applicants. "Having basic math knowledge, especially of decimals, is important because of the precise inputs modern machines need. Like most manufacturers, North American Tool uses CNC, or computer numerical control, equipment. CNC machines make everything from the cutting tool parts North American Tool makes to automotive and medical equipment. But calling these machines computerized is almost a misnomer because there are still plenty of manual calculations. And if you're off, even by a fraction, the equipment can crash." When the CNC machines crash due to human miscalculations, companies like North American Tool incur thousands of dollars to fix the machines, while the work comes to a standstill, meaning lost revenue. Vocational schools, such as Richard J. Daley College in Chicago, teach how to run CNC machines, and algebra and basic trigonometry are prerequisites to enter the program.

According to a recently-published study ("Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety"), researchers studying the impact of math anxiety on girls and boys math performance have found that girls report higher levels of math anxiety and test anxiety than boys, and that "high math anxiety was a stronger predictor of poor test performance for girls than boys." However, the researchers also found "no differences in the girls' overall performance in math, as compared with boys'." The study's authors, Amy Devine, Kayleigh Fawcett, Denes Szucs and Ann Dowker, speculate as to the reasons girls experience higher math anxiety than boys: "that it arises from sex roles that assign math to the male domain; that girls may be more willing to admit feelings of anxiety or may be more critical of themselves than boys; that boys have greater self-confidence; and that past experience with mathematics is responsible." Because math anxiety can cause girls, who have the potential to outperform boys, to develop negative attitudes about math, the authors conclude that mathematics anxiety should be addressed in the classroom.

For Frenkel, a mathematics professor, and Ross, a school superintendent, the recent discovery of the Higgs Boson particle provides a prime example of the importance of mathematical education. While noting that some people believe math is a “dead language” that should receive less attention in the classroom, Frenkel and Ross argue that math is an important building block for nearly every aspect of modern life, from text messages to GPS navigation to particle physics. Based on Frenkel’s recent visit to a classroom, the authors postulate that students exposed to math’s wondrous applications are not bored or scared away, but want to learn more. In order to counter the nationwide backslide in mathematical literacy and the memorization-focused mathematical education plans necessitated by an emphasis on standardized tests, the authors propose increased collaboration between professors and teachers, putting mathematicians in the classroom to paint a picture of mathematical elegance and pique students’ interest.

The recent discovery of the Higgs Boson particle has drawn attention to the particular standard to which physicists hold themselves in using the word "discovery." In physics, in order to prove that a particle exists, researchers must show that the odds that their data resulted from a false positive indication of the particle is less than 1 in 3.5 million, which is known as "five sigmas," in reference to the number of standard deviations from the mean assuming a bell-curve distribution. In contrast, other scientific disciplines, including medicine, require only two or three sigmas. The articles explain that physicists set the bar of proof high because the large amount of data collected allows them to, and because the implications of being wrong---and challenging the fundamental principles of physics---are so daunting. Further complicating matters, physicists must also account for the "Look Elsewhere Effect," which causes researchers to "discover" an unlikely result only because they have looked too hard for it, a phenomenon that has become increasingly likely in the age of computers, which allow greater scrutiny of data.

In this article, Bernard Lane reports on the launching by Cambridge University Press (CUP) of the online, open access mathematics journals Forum of Mathematics, Pi and Forum of Mathematics, Sigma. The former will be a generalist journal, while the latter will publish papers of a more specialized nature. Both journals will follow "the same high levels of peer review process as traditional subscription journals," according to CUP. There will be no charge to authors' institutions to publish their papers for the first three years, after which they will pay between £500 and £700 pounds---"modest by current standards," Lane writes. Submissions will be accepted starting on October 1.

Fields medalist Tim Gowers, whose blog post earlier this year led to the "Cost of Knowledge" boycott of Elsevier, will serve as an editor. "The initial planning for this (CUP) journal happened to precede the boycott," fellow Fields medalist and editor Terence Tao wrote on his blog, "but the philosophy behind the journal is certainly aligned with that of the boycott, which I believe is further evidence that the time has come for mathematical journal reform." See the journal and read about the boycott.

Fernando Codá Marques, National Institute for Pure and Applied Mathematics (IMPA) in Brazil, is the winner of the 2012 Ramanujan Prize for Young Mathematicians from Developing Countries. In 2009 he proved a result that helps in the study of the shape of the universe and this year he and André Neves, Imperial College London, proved the Willmore conjecture (see Brie Finegold's coverage in the April Math Digest). Robert Kusner, University of Massachusetts, Amherst, says, "Fernando is also a fantastic lecturer and a wonderful person to discuss mathematics with,...I can't think of a more deserving recipient of the Ramanujan Prize." (Photo: Roberto Barnaba, ICTP Photo Archives.)

Mathematician John Barrow’s recently published book, 100 Essential Things You Didn’t Know You Didn’t Know About Sport, uses math to explain sports habits from seating order in crew shells to air temperature in bicycle racing arenas. An avid athlete himself, Barrow uses sports examples to make math more enjoyable for his students, which led to the new book. 100 Essential Things explains that world record times in swimming have decreased more dramatically than those in running because swimming coaches are better able to take advantage of mathematical research in fluid dynamics to reduce drag. The book also presents a mathematical formula to explain why a specific pattern of oar placement within a crew shell that is commonly used in competitive racing does, in fact, help a boat move faster than a traditional right-left alternating oar scheme.

Interspersed in this special "Invisible Planet" issue are two pages of mathematical formulas that fall under "The Science You Don't See" sidebar: Prospect theory, Dirac Equation, Exponential Decay, Doppler Equation, and Clocking Evolution. In addition to the mathematical formula, its history and application is explained.